Inference for Network Regression Models with Community Structure
This work addresses inference issues in network regression for social and biological sciences, but it appears incremental as it builds on existing models by incorporating community structure.
The authors tackled the problem of invalid inference in network regression models due to incorrect homogeneity assumptions on errors, by introducing a framework that models errors with community-based dependence structure, resulting in parsimonious standard errors for regression parameters.
Network regression models, where the outcome comprises the valued edge in a network and the predictors are actor or dyad-level covariates, are used extensively in the social and biological sciences. Valid inference relies on accurately modeling the residual dependencies among the relations. Frequently homogeneity assumptions are placed on the errors which are commonly incorrect and ignore critical, natural clustering of the actors. In this work, we present a novel regression modeling framework that models the errors as resulting from a community-based dependence structure and exploits the subsequent exchangeability properties of the error distribution to obtain parsimonious standard errors for regression parameters.